# Write an equation of a line passing through (2, 5), perpendicular to x−5y=−10

Write an equation of a line passing through (2, 5), perpendicular to x−5y=−10
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Kaylee Evans
Let's first look at the the line x−5y=−10 and solve it for y so that we can put it into the slope-intercept form, the general form of which is:
y=mx+b, where m= slope and b= y-intercept.
$x-5y=-10$
$5y=x+10$
$y=\frac{1}{5}x+2$
And so slope, $m=\frac{1}{5}$
To find the perpendicular slope, we take the negative inverse, which gives us m=−5.
To find the line passing through the point (2,5) with slope −5, we can use the point slope form, which has as a general form:
$y-{y}_{1}=m\left(x-{x}_{1}\right)$ where ${x}_{1},{y}_{1}$ are a point. So we have:
(y−5)=−5(x−2)
For comparison, let's put this into slope-intercept form:
y=−5x+15